波束图的球谐族

IF 1.3 Q3 ACOUSTICS
K. Parker, M. Alonso
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引用次数: 0

摘要

众所周知,在球坐标系中波动方程的自由空间解是函数的可分离积。重新检查这些函数,特别是球面贝塞尔函数和调和函数的和,揭示了可以从径向对称源产生一系列有用的光束模式的行为。这些功能可以通过几个关键参数进行修改,这些参数可以调整以产生广泛的光束模式家族,从轴向贝塞尔光束到各种独特的轴向和横向形式。我们证明了球面贝塞尔函数的整数阶简单和的几个特殊性质,以及它们与指定自由空间解的球面调和函数的乘积的和,导致了一系列有用的波束图和一个设计它们的独特框架。从纯音5mhz超声配置的仿真实例中可以看出,该方法具有较强的中心轴集中能力,并且可以通过简单地调整整数阶数和其他与球面贝塞尔函数的权值和参数相关的关键参数来调制或定位轴向强度。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The Spherical Harmonic Family of Beampatterns
The free space solution to the wave equation in spherical coordinates is well known as a separable product of functions. Re-examination of these functions, particularly the sums of spherical Bessel and harmonic functions, reveals behaviors which can produce a range of useful beampatterns from radially symmetric sources. These functions can be modified by several key parameters which can be adjusted to produce a wide-ranging family of beampatterns, from the axicon Bessel beam to a variety of unique axial and lateral forms. We demonstrate that several special properties of the simple sum over integer orders of spherical Bessel functions, and then the sum of their product with spherical harmonic functions specifying the free space solution, lead to a family of useful beampatterns and a unique framework for designing them. Examples from a simulation of a pure tone 5 MHz ultrasound configuration demonstrate strong central axis concentration, and the ability to modulate or localize the axial intensity with simple adjustment of the integer orders and other key parameters related to the weights and arguments of the spherical Bessel functions.
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来源期刊
CiteScore
3.70
自引率
0.00%
发文量
0
审稿时长
11 weeks
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